Uh, no. See, those instructions are from the getting started page. Why do you have to? Because, you can install composer just by downloading it and running it. You dont need to "install" it. This is handy on shared hosting environments where you won't have root.
How can I install bundler on a shared hosting environment like composer?
Well, yes. I can install bundler on a shared hosting environment where I don't have root. In fact, pretty much all my installations are non-root installations. Still, I don't have to manually move it around, symlink or shell-wrap it.
It's not a deal-breaker or a major nuisance that I have to do it, it just fits in what I'm used from php: it gets the job done, but feels unpolished.
You can.
http://getcomposer.org/doc/00-intro.md#globally